On the Stability of Davey-Stewartson System - A Dressing Operator Approach

The problem of stability associated with perturbations around solitonic excitations of Davey-Stewartson equation in three dimension is discussed within the framework of dressing operator approach of Zakharov. The system is stable so far as long time behaviour is concerned and unstable for large transverse directions depending upon the sign of the eigenvalue of the linearized problem.     

Exploring anionic emission of 2-benzoyl benzimidazole in micellar environments

In this paper, an interesting transformation of the emission of anionic conformer of 2-benzoyl bezimidazole in ionic and non-ionic micelles is reported. Deprotonation is hindered in cationic and non-ionic micelles owing to probe molecule's passage deep inside positive ion-rich Stern-layer in contrast with anionic micelle. The orientation of probe molecule in the two ionic micelles, as determined from the spectral properties is opposite in nature. Micellar environment shields the formation of mono- and di-cationic species at very low pH. Three decay times of the probe in different time domains were attributed to three possible anionic species and they are modified differently in ionic and neutral micelles. Quantum chemical calculations also predict the existence of three different possible anionic species.     

Monte Carlo simulation of three-dimensional dilute Ising model

A multispin coding program for site-diluted Ising models on large simple cubic lattices is described in detail. The spontaneous magnetization is computed as a function of temperature, and the critical temperature as a function of concentration is found to agree well with the data of Marro et al.⁽⁴⁾ and Landau⁽³⁾ for smaller systems.The first successful epsilon expansion seems to be by D. E. Khmelnitskii,ZhETF 68:1960 (1975), English translationSov. Phys. JETP 41:981 (1975); for numerical estimates see K. E. Newman and E. K. Riedel,Phys. Rev. H25:264 (1982), for experiments see R. J. Birgenau, R. A. Cowley, G. Shirane and H. Yoshizawa,J. Stat. Phys. 34:817 (1984).     

Synthesis,X‐ray powder structure analysis and biological properties of a mononuclear Cu(II) complex of N‐2‐hydroxyhippuric acid

A mononuclear copper (II) complex of N‐2‐hydroxyhippuric acid (2HHA), [Cu(HA)(H₂O)₂], has been synthesized and characterized by spectroscopic and X‐ray powder diffraction studies. Crystal structure of [Cu(HA)(H₂O)₂] reveals a distorted square‐pyramidal geometry around the metal center. The crystal packing in the complex exhibits a three‐dimensional framework formed by intermolecular O? ; H···O and C? H···O hydrogen bonds. Toxicity and antitumor properties of the complex have been studied in vivo. The complex, capable of depleting glutathione (GSH) at nontoxic doses, may be utilized to sensitize drug‐resistant cells where resistance is due to an elevated level of GSH. Copyright © 2009 John Wiley & Sons, Ltd.     

New coupled Liouville system: Prolongation structure,soliton solution,and complete integrability

We suggest a new coupled Liouville equation which is exactly solvable. We obtain the Lax pair through a prolongation analysis and also obtain the exact one-soliton-like solution by a direct procedure. We confirm our result through a Painlevé analysis of the similarity reduced systems.     

Two manganese(II) coordination polymers driven by (iso)nicotinoyl-hydrazone blocks and pseudohalide ancillary ligands: syntheses,structural features,and magnetic properties

Two coordination polymers, [Mn₂(μ-L¹)₂(μ-N₃)₂]_n (1) and [Mn(μ-HL²)(SCN)₂]_n (2), were assembled in a single-pot from MnCl₂·4H₂O, HL¹ (2-acetylpyridine isonicotinoylhydrazone) or HL² (2-acetylpyridine nicotinoylhydrazone) and ancillary ligand sources (NaN₃ or NH₄NCS). The products were fully characterized, including by single-crystal X-ray diffraction, which revealed a 2-D metal–organic layer in 1 and a 1-D zigzag coordination chain in 2. Both 1 and 2 are constructed from six-coordinate Mn(II) nodes that adopt distorted octahedral (MnN₅O) environments; the adjacent nodes are driven by the μ-L¹ and μ-N₃ linkers in 1 or μ-HL² linkers in 2 to form different metal–organic networks. Their topological classification was performed, disclosing the hcb and 2C1 topology in 1 and 2, respectively. Different weak non-covalent interactions promote dimensionality extension. Variable-temperature magnetic susceptibility measurements were carried out, revealing weak ferromagnetic and antiferromagnetic interactions in 1 and 2, respectively.     

Structural Characterization of Coordination Polymers of Nickel(II) and Zinc(II) with Polycarboxylate Ligands

Abstract  

The structural aspects of one-dimensional coordination polymer (1) of nickel(II) with 1,3,5-benzene tricarboxylate and a three-dimensional interpenetrating coordination polymer (2) of zinc(II) with 1,4-benzenedicarboxylate ligand are studied by single crystal X-ray diffraction analysis. Coordination polymer (1) forms a hydrogen bonded three dimensional network structures. The coordination polymer 1 having a composition [Ni₃(TMA)₂(H₂O)₁₂] _n where (TMA = trimesate anion), crystallizes in monoclinic crystal system with C2 space group and has a/?, 17.3387(4); b/?, 12.8748(4); c/?, 6.5302(2); β/°111.620(2); V/?³, 1355.20(7). The zinc coordination polymer 2 crystal system is orthorhombic, with space group Pbca. It has a/?, 14.5049(3); b/?, 17.1616(3); c/?, 18.1389(4); V/?³, 4515.27(16). The 1,4-benzenedicarboxylate three dimensional coordination polymer of zinc(II) comprises of novel hydroxo bridged tetranuclear zinc(II) secondary building units and has a composition [Zn₂(C₆H₄C₂O₄)_1.5{(CH₃)₂SO}₂(OH)] _n . Topological analysis of the three dimensional coordination polymer 2 shows that it has a two fold interpenetrating net topology.     

Graphical Representations of Speed: Obstacles Preservice K‐8 Teachers Experience

This study examines the difficulties college students experience when creating and interpreting graphs in which speed is one of the variables. Nineteen students, all preservice elementary or middle school teachers, completed an upper‐level course exploring algebraic concepts. Although all of these preservice teachers had previously completed several mathematics courses, including calculus, they demonstrated widespread misconceptions about the variable speed. This study identifies four cognitive obstacles held by the students, provides excerpts of their graphical constructions and verbal interpretations, and discusses potential causes for the confusion. In particular, misconceptions arose when students interpreted the behavior and nature of speed within a graphical context, as well as in situations where they were required to construct a graph involving speed as a variable. The study concludes by offering implications for the teaching and learning of speed and its interpretation within a graphical setting.